Dubravka has three years remaining on his current deal but despite impressing since arriving in the North East, remains one of the club's lowest earners.
Speaking after the defeat to Liverpool on Saturday, the Slovakian goalkeeper said: "We're in talks. I'm close. We are in contact and hopefully we can sort it out as soon as possible.
"I'm happy here so if I can stay longer here, I will be happy. Since I came here, people have treated me really well. I can say that I feel at home here.
"I'm glad that people think that I can stay here for the longer term. It's such a big honour for me."